In the carbon cycle, carbon in the atmosphere is absorbed into plants, where the plants use photosynthesis to convert that carbon into oxygen and energy for themselves. Neither of the other cycles involves a plant taking in a gas directly from the atmosphere.
Whether a cell uses facilitated diffusion or active transport depends on the specific needs of the cell. For example, the sugar glucose is transported by active transport from the gut into intestinal epithelial cells, but by facilitated diffusion across the membrane of red blood cells.
